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Abstract

A description is given of the properties of plane diffraction gratings used in conical diffraction. Formulas are given for computing the direction of the diffracted orders. Experiments were performed to investigate the behavior of gratings used on conical diffraction mountings. Comparisons made with classical diffraction mountings show a significant increase in the efficiency of the −1 order. An empirical formula to predict the efficiencies of gratings used in conical diffraction mountings has been verified by the measurements.

References

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TABLE I

Comparison of a geometric factor τ, obtained from Eq. (13), to the ratio ρ of measured efficiencies in the classical RWF mount to the GMS mount for a gold grating with blaze angle 2°4′. [Note that ϕ (or θ″) is given by λ = 2d sinδ cosϕ.]

λ (Å)

θ″ (or ϕ) (deg.)

τ

ρ

556

62.45

0.871

0.94

405

70.31

0.817

0.77

305

75.30

0.758

0.77

247

78.14

0.707

0.67

217

79.60

0.671

0.68

198

80.52

0.645

0.62

TABLE II

Comparison of a geometric factor τ, obtained from Eq. (13), to the ratio ρ of measured efficiencies in the classical RWF mount to the GMS mount for a gold grating with blaze angle 9°19′. [Note that ϕ (or θ″) is given by λ = 2d sinδ cosϕ.]

λ (Å)

θ″ (or ϕ) (deg.)

τ

ρ

835

62.34

0.523

0.59

711

66.71

0.448

0.44

640

69.16

0.398

0.41

555

72.03

0.328

0.30

TABLE III

Comparison of a geometric factor τ, obtained from Eq. (13), to the ratio of measured efficiencies in the classical mount to a conical diffraction mount wherein the grating has been rotated through an angle ψ = 30° from the GMS mount. Note that τ = min [cos θ′/cos θ, cos θ/cos θ′], and can be calculated from values obtained from Eq. (14).

λ (Å)

θ″ (or ϕ) (deg.)

τ

ρ

835

62.34

0.729

0.78

711

66.71

0.680

0.77

640

69.16

0.645

0.74

555

72.03

0.596

0.64

492

74.13

0.552

0.56

414

76.69

0.485

0.50

TABLE IV

Comparison of a geometric factor τ, obtained from Eq. (13), to the ratio of measured efficiencies in the classical mount to a conical diffraction mount wherein the grating has been rotated through an angle ψ = 60° from the GMS mount. Note that τ = min [cos θ′/cos θ, cos θ/cos θ′], and can be calculated from values obtained from Eq. (14).

λ (Å)

θ″ (or ϕ) (deg.)

τ

ρ

835

62.34

0.574

0.64

711

66.71

0.504

0.51

640

69.16

0.456

0.46

555

72.03

0.391

0.39

492

74.13

0.334

0.30

414

76.69

0.250

0.19

Tables (4)

TABLE I

Comparison of a geometric factor τ, obtained from Eq. (13), to the ratio ρ of measured efficiencies in the classical RWF mount to the GMS mount for a gold grating with blaze angle 2°4′. [Note that ϕ (or θ″) is given by λ = 2d sinδ cosϕ.]

λ (Å)

θ″ (or ϕ) (deg.)

τ

ρ

556

62.45

0.871

0.94

405

70.31

0.817

0.77

305

75.30

0.758

0.77

247

78.14

0.707

0.67

217

79.60

0.671

0.68

198

80.52

0.645

0.62

TABLE II

Comparison of a geometric factor τ, obtained from Eq. (13), to the ratio ρ of measured efficiencies in the classical RWF mount to the GMS mount for a gold grating with blaze angle 9°19′. [Note that ϕ (or θ″) is given by λ = 2d sinδ cosϕ.]

λ (Å)

θ″ (or ϕ) (deg.)

τ

ρ

835

62.34

0.523

0.59

711

66.71

0.448

0.44

640

69.16

0.398

0.41

555

72.03

0.328

0.30

TABLE III

Comparison of a geometric factor τ, obtained from Eq. (13), to the ratio of measured efficiencies in the classical mount to a conical diffraction mount wherein the grating has been rotated through an angle ψ = 30° from the GMS mount. Note that τ = min [cos θ′/cos θ, cos θ/cos θ′], and can be calculated from values obtained from Eq. (14).

λ (Å)

θ″ (or ϕ) (deg.)

τ

ρ

835

62.34

0.729

0.78

711

66.71

0.680

0.77

640

69.16

0.645

0.74

555

72.03

0.596

0.64

492

74.13

0.552

0.56

414

76.69

0.485

0.50

TABLE IV

Comparison of a geometric factor τ, obtained from Eq. (13), to the ratio of measured efficiencies in the classical mount to a conical diffraction mount wherein the grating has been rotated through an angle ψ = 60° from the GMS mount. Note that τ = min [cos θ′/cos θ, cos θ/cos θ′], and can be calculated from values obtained from Eq. (14).